Analysis of the contribution of skeletal vibrations to the heat capacity of linear macromolecules in the solid state

Automatic computer programs are developed to calculate one- two-, and three-dimensional Debye functions. Prior tables of these functions are critically reviewed. Also, strategies are derived to calculate Debye temperatures from heat capacities. Both, simple three-dimensional Debye analyses and Tarasov analyses were carried out on 35 linear macromolecules. The experimental heat capacities for these analyses were collected in the ATHAS data bank. It is shown that the skeletal heat capacity of linear macromolecules is often best represented by only two vibrations per chain atom. For most of the all-carbon chain macromolecules the intramolecular skeletal heat capacity can be given by C_vs=D₁[520 (28/MW)^1/2] whereMW is the molecular mass andD ₁ represents the one-dimensional Debye function. Polyoxides show a higher intramolecular theta temperature, but a lower intermolecular theta temperature. Double bonds and phenylene groups in the chain increase the intramolecular theta temperature.Dedicated to Prof. Dr. F. H. Müller.On leave from the Lumumba Peoples' Friendship University, Moscow, USSR.     

Specific heat of molecular crystals from atomic mean square displacements with the Einstein, Debye, and Nernst-Lindemann models

Analysis of atomic displacement parameters (ADPs) from multitemperature diffraction data provides mean-field molecular translation and libration frequencies. These quantities have been combined with molecular deformation frequencies calculated ab initio, e.g. by DFT methods, to calculate the specific heat Cv of molecular crystals of naphthalene, anthracene, and hexamethylenetetramine. If the difference Cp - Cv is represented by the Nernst-Lindemann relation, Cp curves from diffraction experiments and ab initio calculations agree well with those based on calorimetry. Agreement is better if the Debye rather than the Einstein model is chosen to represent the contribution of the translational vibrations. Compressibilities estimated from the differences Cp - Cv are 2-5 times higher than those obtained from compressibility measurements at 298 K and Grüneisen constants derived from the temperature dependence of ADPs.     

TiO_2的相变和热力学性质(英文)

利用第一性原理平面波赝势密度泛函理论方法对TiO2从金红石结构到萤石结构的相变进行了理论研究,并且通过准谐德拜模型分别得到了金红石和萤石结构TiO2的热力学性质.计算结果与实验值以及其它理论计算的结果都符合得很好,通过吉布斯能的计算得到TiO2从金红石结构到萤石结构的相变压强为47.74GPa,并成功地获得了相对体积(V/V0)、德拜温度(Θ)和热容(CV)随压强(p)和温度(T)的变化关系.     

The role of the ice rules in the thermal properties of potassium dihydrogen phosphate

Calorimetric properties of potassium dihydrogen phosphate are examined by analysis of the heat capacity data taken from the literature and from a recent measurement. The analysis is based on an extensive use of harmonic heat capacity functions to separate the effect of the phase transition from the vibrational contribution. The transition enthalpy and entropy derived are 421 J mol^–1 and 3.79 J K^–1 mol^–1, respectively. Characteristic temperatures of the lattice vibrations including the Debye temperature (254±18) K were determined. The transition entropy, exceeding the value compatible with the ice-rules, is consistent with the temperature dependence of the heat capacity. The implication of the result is discussed by comparison with the hydrogen bond networks in copper formate tetrahydrate and thallium dihydrogen phosphate.Dedicated to Professor Bernhard Wunderlich on the occasion of his 65th birthdayContribution No. 113 from Microcalorimetry Research Center.     

The phonon heat capacity of diborides: The approximation of interacting sublattices

The temperature dependence of the heat capacity of structures formed by alternating layers with different atomic compositions is described using the model of interacting three- and two-dimensional Debye sublattices. The parameters of the model are the characteristic temperatures Θ₁ and Θ₃ of the sublattices and the characteristic temperature Θ₂ corresponding to vibrations between the sublattices. (In the accepted approximation, Θ₂ equals the characteristic Debye temperature of the substance at absolute zero.) The model was used to analyze the temperature dependences of the lattice (phonon) heat capacities of transition and rare-earth metal diborides MB₂. This allowed the characteristic temperatures Θ _i and trends of their variations depending on metal atomic numbers to be determined.     

Analysis of the residual entropy of amorphous polyethylene at 0 K*

The residual entropy of amorphous polyethylene (PE) at 0 K is discussed within the framework of the heat capacity (C_p). The measured C_p of the liquid was extended from the glass transition to low temperature by separately finding its three parts—the vibrational, conformational, and external contributions—and extrapolating each to low temperature. The vibrational C_p was calculated from the frequency distributions of the group vibrations on the basis of force constants obtained from experimental infrared and Raman spectra as well as the skeletal vibrations in the amorphous solid (glass) obtained from fitting of the appropriate experimental C_p to Debye functions in the form suggested by Tarasov. The conformational part of C_p was evaluated from a fit of the heat capacity of the liquid, decreased by the contributions of the vibrational and external parts, to a one‐dimensional Ising model that can be extrapolated to 0 K and requires two discrete states described by stiffness, cooperativity, and a degeneracy parameter. The external part was computed from the experimental data for expansivity and compressibility, fitted to an empirical equation of state, and modified at low temperatures in accordance with the Nernst–Lindemann approximation. The computed C_p of the liquid PE agreed with the experiment from 600 K to the beginning of the glass transition at about 260 K. Extending the heat capacity to 0 K, bypassing the freezing of the large‐amplitude conformational motion in the glass transition, led to a positive residual entropy and enthalpy and avoided the so‐called Kauzmann paradox. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1245–1253, 2002     

Phonon spectrum of a fluorene molecular crystal

The dynamics of the fluorene molecular crystal lattice is calculated by the atom-atom potential method. The fundamental lattice vibration frequencies are determined, their assignment is made, and shapes of the vibrations are studied over a pressure range of from 1 bar to 30 kbar. For acoustic phonon vibrations, the distribution of Debye frequencies over directions of the wave vector is estimated. The results obtained are used to discuss the photochemical reaction of detachment of a hydrogen atom in a fluorene crystal, a process occurring by the tunneling mechanism.     

Thermal-diffusive behavior of a dilute solution of charged colloids

Thermal diffusion of a dilute solution of charged silica colloidal particles (Ludox) is studied by a holographic grating technique. The Soret coefficient of the charged colloids is measured as a function of the Debye screening length and the surface charge density of the colloids. The latter is varied by means of variation of the pH. The experimental Soret coefficients are compared with several theoretical predictions. The surface charge density is independently obtained from electrophoresis measurements, the size of the colloidal particles is obtained from electron microscopy, and the Debye length is calculated from ion concentrations. The only adjustable parameter in the comparison with theory is therefore the intercept at zero Debye length, which measures the contribution to the Soret coefficient of the solvation layer and possibly the colloid core material.     

EuS高压相变发其弹性和热力学性质

采用平面波赝势密度泛函理论,利用第一性原理的方法研究了EuS的晶体结构、高压相变以及弹性性质．计算结果和实验值以及前人利用不同计算模型得到的理论值相吻合．研究了EuS的弹性常数、弹性模量和弹性的各向异性等力学性质随压力变化的趋势．同时研究了泊松比、德拜温度及纵波和横波的弹性波速随压力的变化趋势．基于德拜模型,进而研究了EuS在0-800K和0-60GPa下相变前后的热膨胀系数、热熔、Gruneisen参数等热力学性质．     

Thermal Expansion Behaviors of Li3AsW7O25: A Case Study for Comparative Debye Temperature for a Large Polyatomic Unit Cell

The thermal expansion behavior of Li₃AsW₇O₂₅ has been studied. The temperature‐dependent development of crystal structural parameters was obtained from Rietveld refinement using neutron time of flight powder diffraction data. Modeling of the lattice thermal expansion was carried out using a Grüneisen first‐order approximation for the zero‐pressure equation of state, where the temperature‐dependent vibrational energy was calculated taking the Debye‐Einstein‐Anharmonicity approach. Temperature‐dependent Raman spectra shed light on some selective modes with unusual anharmonicity. Debye temperatures were calculated using three different theoretical approaches, namely, thermal expansion, mean‐squared isotropic atomic displacement parameter and heat capacity. Similarities as well as discrepancies between the numerical values obtained from different theoretical approaches are discussed.     

Elastic Tensor and Thermodynamic Property of Magnesium Silicate Perovskite from First-principles Calculations

The thermodynamic and elastic properties of magnesium silicate (MgSiO₃) perovskite at high pressure are investigated with the quasi-harmonic Debye model and the first-principles method based on the density functional theory. The obtained equation of state is consis-tent with the available experimental data. The heat capacity and the thermal expansion coefficient agree with the observed values and other calculations at high pressures and tem-peratures. The elastic constants are calculated using the finite strain method. A complete elastic tensor of MgSiO₃ perovskite is determined in the wide pressure range. The geo-logically important quantities: Young's modulus, Poisson's ratio, Debye temperature, and crystal anisotropy, are derived from the calculated data.     

The structural,electronic, elastic,vibration and thermodynamic properties of GdMg

We have investigated the structural, elastic, electronic, vibration and thermodynamic properties of GdMg alloy using the methods of density functional theory within the generalized gradient approximation (GGA) for the exchange-correlation functional. We have presented the results on the basic physical parameters, such as the lattice constant, bulk modulus, pressure derivative of bulk modulus with and without spin-polarization (SP), second-order elastic constants, Zener anisotropy factor, Poisson's ratio, Young's modulus, and isotropic shear modulus. The thermodynamic properties of the considered compound are obtained through the quasi-harmonic Debye model. In order to obtain further information, we have also studied the pressure and temperature-dependent behavior of the volume, bulk modulus, thermal expansion coefficient, heat capacity, and Debye temperature in a wide temperature range of 0–1200 K. We have also calculated phonon frequencies and one-phonon density of states for B2 structure of GdMg compound. The temperature-dependent behavior of heat capacity and entropy obtained from phonon density of states for GdMg compound in B2 phase is also presented.     

Phase transition and thermodynamic properties of TiN under pressure via first-principles calculations

The phase transition of TiN from the NaCl structure to the CsCl structure is investigated by the first-principles plane wave pseudopotential density functional theory method, and the thermodynamic properties of the NaCl structures are obtained through the quasi-harmonic Debye model. It is found that the pressures for transition from the NaCl structure to the CsCl structure are 364.1 GPa (for GGA) and 322.2 (for LDA) from equal enthalpies. The calculated ground state properties such as equilibrium lattice constant, bulk modulus, and its pressure derivative are in good agreement with experimental and theoretical data of others. Moreover, the dependences of the relative volume V/V ₀ on the pressure P, the Debye temperature ?? _D , and heat capacity C _V on the pressure P and temperature T, as well as the variation of the thermal expansion ?? with temperature and pressure are also successfully obtained.     

Thermal broadening of the J-band in disordered linear molecular aggregates: a theoretical study

We theoretically study the temperature dependence of the J-band width in disordered linear molecular aggregates, caused by dephasing of the exciton states due to scattering on vibrations of the host matrix. In particular, we consider inelastic one- and two-phonon scatterings between different exciton states (energy-relaxation-induced dephasing), as well as the elastic two-phonon scattering of the excitons (pure dephasing). The exciton states follow from numerical diagonalization of a Frenkel exciton Hamiltonian with diagonal disorder; the scattering rates between them are obtained using the Fermi golden rule. A Debye-type model for the one- and two-phonon spectral densities is used in the calculations. We find that, owing to the disorder, the dephasing rates of the individual exciton states are distributed over a wide range of values. We also demonstrate that the dominant channel of two-phonon scattering is not the elastic one, as is often tacitly assumed, but rather comes from a similar two-phonon inelastic scattering process. In order to study the temperature dependence of the J-band width, we simulate the absorption spectrum, accounting for the dephasing-induced broadening of the exciton states. We find a power-law (T(p)) temperature scaling of the effective homogeneous width, with an exponent p that depends on the shape of the spectral density of the host vibrations. In particular, for a Debye model of vibrations, we find p approximately 4, which is in good agreement with the experimental data on J aggregates of pseudoisocyanine [I. Renge and U. P. Wild, J. Phys. Chem. A, 101, 7977 (1997)].     

3C-SiC的结构和热力学性质

利用第一性原理平面波模守恒赝势密度泛函理论研究了3C-SiC的结构, 其零温(0 K)零压下的晶格常数、体弹模量及其对压强的一阶导数、弹性常数的计算结果与实验值和其它理论计算结果相符合. 通过准谐德拜模型, 得到了不同温度不同压强下的热容和德拜温度, 发现热容随着压强增加而减小, 德拜温度随压强增加而增加, 并成功地获得了相对晶格常数、相对体积、体弹模量、热膨胀系数与温度和压强的关系.     

Effective Debye length in closed nanoscopic systems: a competition between two length scales

The Poisson-Boltzmann equation (PBE) is widely employed in fields where the thermal motion of free ions is relevant, in particular in situations involving electrolytes in the vicinity of charged surfaces. The applications of this non-linear differential equation usually concern open systems (in osmotic equilibrium with an electrolyte reservoir, a semi-grand canonical ensemble), while solutions for closed systems (where the number of ions is fixed, a canonical ensemble) are either not appropriately distinguished from the former or are dismissed as a numerical calculation exercise. We consider herein the PBE for a confined, symmetric, univalent electrolyte and quantify how, in addition to the Debye length, its solution also depends on a second length scale, which embodies the contribution of ions by the surface (which may be significant in high surface-to-volume ratio micro- or nanofluidic capillaries). We thus establish that there are four distinct regimes for such systems, corresponding to the limits of the two parameters. We also show how the PBE in this case can be formulated in a familiar way by simply replacing the traditional Debye length by an effective Debye length, the value of which is obtained numerically from conservation conditions. But we also show that a simple expression for the value of the effective Debye length, obtained within a crude approximation, remains accurate even as the system size is reduced to nanoscopic dimensions, and well beyond the validity range typically associated with the solution of the PBE.     

In situ temperature-modulated microscopy observation of two-phase co-existing states of coumarin and coumarin derivative in melting

Coumarin (C₉H₆O₂) and coumarin derivative, coumarin 6H (C₁₅H₁₅NO₂) samples were observed with a polarizing microscope at and around the melting points. The states of the two samples are crystalline at room temperature. When the temperature of the Coumarin sample was raised and a part was melted, the crystalline phases coexisted with the liquid phase. The crystal surface coexisting with the liquid phase went through a repetition of melting and crystallization on slightly modulating the sample temperature. The two-phase coexisting state was observed with a digital camera attached to a microscope. The changes in the number of pixels in the crystal part of the photographed image showed Debye relaxation with temperature change. It was found that the relaxation time was 4.9 s when the number of pixels decreased due to surface melting or increased due to surface crystallization. This relaxation time was in good agreement with that of the dynamic-specific heat measured by AC calorimetry. The coumarin 6H microcrystal also coexisted with the melt in a temperature range at and around the melting point. The change in the number of pixels of the coumarin 6H crystal part showed Debye relaxation with respect to the temperature, and the relaxation time was 15 s, which was the same as the relaxation time of the dynamic-specific heat measured in the melting temperature range of coumarin 6H.

     

Pressure and temperature dependence of H-atom tunneling in the Debye approximation. Barrier preparation and media reorganization

In the frame of the radiationless transitions modified theory, the analytical expression of a rate constant of the chemical reaction with an atom tunneling is found for the case of a continuous spectrum of a phonon subsystem. Two mechanisms of temperature dependence of a rate constant are taken into account, the oscillations of the potential barrier of the reaction at the intermolecular vibrations and media reorganization. The simple expressions for temperature and pressure dependencies of a rate constant are obtained in the special case of lattice motion-the Debye model. The well-known Marcus expression for the rate constant of an electron transfer in the Debye phonon spectrum is deduced first. The pressure dependence of the reorganization energy of the media is derived. Comparison of the theoretical results with the literature experimental data on H-atom tunneling in the fluorene-acridine crystal, taking into account four promotive modes (translational, librational, and two low-frequency intramolecular modes at 95 and 238 cm(-1)) and the frequency dependence of the Grueneisen parameter, is fulfilled. Good agreement of the theory and experiments is observed.     

Heat capacity of poly(vinyl methyl ether)

The heat capacity of poly(vinyl methyl ether) (PVME) has been measured using adiabatic calorimetry and temperature‐modulated differential scanning calorimetry (TMDSC). The heat capacity of the solid and liquid states of amorphous PVME is reported from 5 to 360 K. The amorphous PVME has a glass transition at 248 K (?25 °C). Below the glass transition, the low‐temperature, experimental heat capacity of solid PVME is linked to the vibrational molecular motion. It can be approximated by a group vibration spectrum and a skeletal vibration spectrum. The skeletal vibrations were described by a general Tarasov equation with three Debye temperatures Θ₁ = 647 K, Θ₂ = Θ₃ = 70 K, and nine skeletal modes. The calculated and experimental heat capacities agree to better than ±1.8% in the temperature range from 5 to 200 K. The experimental heat capacity of the liquid rubbery state of PVME is represented by C_p(liquid) = 72.36 + 0.136 T in J K^?1 mol^?1 and compared to estimated results from contributions of the same constituent groups of other polymers using the Advanced Thermal AnalysiS (ATHAS) Data Bank. The calculated solid and liquid heat capacities serve as baselines for the quantitative thermal analysis of amorphous PVME with different thermal histories. Also, knowing C_p of the solid and liquid, the integral thermodynamic functions of enthalpy, entropy, and free enthalpy of glassy and amorphous PVME are calculated with help of estimated parameters for the crystal. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2141–2153, 2005